Many card cheaters tricks are based on the shuffling of the deck.
Collecting the cards from the table and shuffling the deck in
a special way, the cheater may get the desired order of
the cards. In this problem you have to model the process to
see that the cheater can often reach his goal.

The deck contains n cards.
The shuffling consists of exactly t moves.
There are p ways to make each move.
The i-th way to make some move is the following.
The shuffler picks mi + li cards from the top of the deck and moves
them to the bottom of the deck. There he drops the last li cards picked,
letting them stay at the bottom of the deck, and returns the other mi
cards to the top of the deck. The order of the cards within the
blocks of li and mi cards, and the cards staying in the deck remains the same.

Given the initial order of the cards in the deck, the desired order,
and the parameters of the shuffle, find out whether it is possible
to reorder the cards in the specified way.

Input

The first line of the input file contains n, t, and p
(2 ≤ n ≤ 36, 1 ≤ t ≤ 15, 1 ≤ p ≤ 5).
The next two lines contain the initial and the desired order of the
cards respectively. Cards are identified by integer numbers
from 1 to n, all cards are different,
the cards are listed from the bottom of the deck to its top.

Output

If it is impossible to reoreder the cards in the required way using exactly
t shuffling moves, output "Impossible"" on the first line of the
output file. In the other case output t integer numbers --- in which
way to perform each move.